Consider a two-person (1 and 2) two good (X and Y) exchange economy. The utility function of person 1 is given by U1 = A1 x1 - b1 x1^2 + y1 and the utility function of person 2 is given by U2 = A2 x2 - b2 x 2^2 + y2 where xi and yi denote respectively person i's the consumption amount of good X and good Y, i = 1, 2. Let A1 = 231, b1 = 1/2, A2 = 231 and b 2 = 1/8 be the values of the parameters above. Suppose the economy has a total of 108 units of good X and 85060 units of good Y What is the value of the marginal rate of substitution of person 1 when each person has the efficient amount of good X ?

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The small open economy case We consider a small open economy producing two goods i=1,2. These goods are produced using only one factor of production, labor. We will denote by a the quantity of labor required for the production of one unit of good i. We will denote by L the labor endowment of the country. The representative consumer in the country has preferences given by the utility function U (C₁, C₂) = a Log C₁ + (1 -a) Log C₂ We let p; denote the price of good i and w, denote the wage rate in sector i. 1. Derive the relationship determining the competitive supply of this econ- omy, given by the vector Q= (Q1, Q2) of produced quantities of both goods, as a function of prices p₁ and p2. Represent graphically the rela- tive supply schedule of good 1, as a function of the relative price Determine the labor market clearing rate w. 2. Represent graphically the set of feasible output combinations (the Pro- duction Possibilities Set) in the (Q₁, Q2) space. How is the competitive relative…